Question: Solve for $x$ and $y$ using elimination. ${4x-y = 33}$ ${-5x+y = -42}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-x = -9$ $\dfrac{-x}{{-1}} = \dfrac{-9}{{-1}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {4x-y = 33}\thinspace$ to find $y$ ${4}{(9)}{ - y = 33}$ $36-y = 33$ $36{-36} - y = 33{-36}$ $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ You can also plug ${x = 9}$ into $\thinspace {-5x+y = -42}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ + y = -42}$ ${y = 3}$